Case-scale analysis

Pair-wise correlations

Latitud

Age

Altitud

BMI

Diabetes

Hypertension

Sugar

Vitamin D

Multiple regression

Response variable = vit D
Explanatory variables = bmi, lat, alt

Impossible: not enough observations.

Municipal-scale analysis

Pair-wise correlations

Deaths per 100,000

Altitude

Latitude

Ethnicity

Mean Vit D

nmol < 30

nmol < 50

nmol < 75

Multivariate regression 1

Response variable = mean Vit D
Explanatory variables = Deaths per 100,000, Altitude, Latitude, & Ethnicity

## 
## Call:
## lm(formula = mean_vitD ~ Deaths_ht + Alt + Lat + Ethnicity, data = df_mun)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.2290  -3.7819   0.1014   3.3563  17.7267 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) 88.9040762  4.0115430  22.162  < 2e-16 ***
## Deaths_ht   -0.0654517  0.0284264  -2.302   0.0227 *  
## Alt         -0.0064036  0.0005495 -11.654  < 2e-16 ***
## Lat         -0.8637112  0.1594275  -5.418 2.48e-07 ***
## Ethnicity   -0.0303885  0.0383118  -0.793   0.4290    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.539 on 144 degrees of freedom
## Multiple R-squared:  0.5685, Adjusted R-squared:  0.5565 
## F-statistic: 47.43 on 4 and 144 DF,  p-value: < 2.2e-16

Explanatory variables, together, explain 30% of the variance in Vit D at municipal scale. When controlling for other variables, each variable shows a negative relation with vit D, but only deaths per 100,000, altitude, and latitude are significant. If ethnicity is removed from the model, results are almost the same in terms of coefficients, their signs, and R2.

Multivariate regression 2

Response variable = Deaths per 100,000
Explanatory variables = Altitude and Latitude

## 
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat, data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -37.684 -10.062  -1.104   6.567  59.323 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -19.261431   8.301666  -2.320   0.0217 *  
## Alt           0.003873   0.001502   2.579   0.0109 *  
## Lat           2.038969   0.354502   5.752    5e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 16.13 on 146 degrees of freedom
## Multiple R-squared:  0.1922, Adjusted R-squared:  0.1811 
## F-statistic: 17.37 on 2 and 146 DF,  p-value: 1.712e-07

Multivariate regression 3

Response variable = Deaths per 100,000
Explanatory variables = Altitude, Latitude, nmol < 30

## 
## Call:
## lm(formula = Deaths_ht ~ Alt + Lat + nmol_30, data = df_mun)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -39.308  -9.256  -1.324   7.033  56.424 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -14.954767   8.242257  -1.814  0.07168 .  
## Alt           0.002704   0.001521   1.778  0.07758 .  
## Lat           1.775510   0.358072   4.959 1.96e-06 ***
## nmol_30      88.748859  30.976930   2.865  0.00479 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 15.75 on 145 degrees of freedom
## Multiple R-squared:  0.2355, Adjusted R-squared:  0.2197 
## F-statistic: 14.89 on 3 and 145 DF,  p-value: 1.683e-08